LMFDB - Embedded newform 1096.1.z.a.1027.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(11,1096)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1096, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 34, 61]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1096.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.z (of order $68$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.546975253846$
Analytic rank:	$0$
Dimension:	$32$
Coefficient field:	$\Q(\zeta_{68})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \cdots + 1 $ x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{68}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{68} - \cdots)$

Embedding invariants

Embedding label			1027.1
Root			$0.183750 - 0.982973i$ of defining polynomial
Character	$\chi$	$=$	1096.1027
Dual form			1096.1.z.a.683.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673696 - 0.739009i) q^{2} +(0.453510 + 1.92821i) q^{3} +(-0.0922684 + 0.995734i) q^{4} +(1.11943 - 1.63417i) q^{6} +(0.798017 - 0.602635i) q^{8} +(-2.61715 + 1.30318i) q^{9} +O(q^{10})$	\(q+(-0.673696 - 0.739009i) q^{2} +(0.453510 + 1.92821i) q^{3} +(-0.0922684 + 0.995734i) q^{4} +(1.11943 - 1.63417i) q^{6} +(0.798017 - 0.602635i) q^{8} +(-2.61715 + 1.30318i) q^{9} +(-1.95756 - 0.181395i) q^{11} +(-1.96183 + 0.273663i) q^{12} +(-0.982973 - 0.183750i) q^{16} +(0.293271 + 0.221468i) q^{17} +(2.72622 + 1.05614i) q^{18} +(-0.576554 + 1.48826i) q^{19} +(1.18475 + 1.56886i) q^{22} +(1.52391 + 1.26544i) q^{24} +(0.995734 - 0.0922684i) q^{25} +(-2.43427 - 2.93148i) q^{27} +(0.526432 + 0.850217i) q^{32} +(-0.538007 - 3.85684i) q^{33} +(-0.0339085 - 0.365931i) q^{34} +(-1.05614 - 2.72622i) q^{36} +(1.48826 - 0.576554i) q^{38} +(-0.323785 + 0.323785i) q^{41} +(0.456541 + 1.03397i) q^{43} +(0.361242 - 1.93247i) q^{44} +(-0.0914812 - 1.97871i) q^{48} +(0.850217 - 0.526432i) q^{49} +(-0.739009 - 0.673696i) q^{50} +(-0.294034 + 0.665924i) q^{51} +(-0.526432 + 3.77387i) q^{54} +(-3.13114 - 0.436776i) q^{57} +(0.658809 + 1.32307i) q^{59} +(0.273663 - 0.961826i) q^{64} +(-2.48779 + 2.99593i) q^{66} +(0.241393 + 0.134455i) q^{67} +(-0.247582 + 0.271585i) q^{68} +(-1.30318 + 2.61715i) q^{72} +(-0.288130 + 1.01267i) q^{73} +(0.629488 + 1.87814i) q^{75} +(-1.42871 - 0.711414i) q^{76} +(2.78663 - 3.69010i) q^{81} +(0.457413 + 0.0211475i) q^{82} +(0.134455 - 0.963876i) q^{83} +(0.456541 - 1.03397i) q^{86} +(-1.67148 + 1.03494i) q^{88} +(-0.0373089 - 0.806980i) q^{89} +(-1.40065 + 1.40065i) q^{96} +(-1.18375 + 0.982973i) q^{97} +(-0.961826 - 0.273663i) q^{98} +(5.35961 - 2.07632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times$.

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{29}{68}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$2$	−0.673696	−	0.739009i	−0.673696	−	0.739009i
$3$	0.453510	+	1.92821i	0.453510	+	1.92821i	0.361242	+	0.932472i	$0.382353\pi$
$3$	0.453510	+	1.92821i	0.453510	+	1.92821i	0.0922684	+	0.995734i	$0.470588\pi$
$4$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$5$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$5$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$6$	1.11943	−	1.63417i	1.11943	−	1.63417i
$7$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$7$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$8$	0.798017	−	0.602635i	0.798017	−	0.602635i
$9$	−2.61715	+	1.30318i	−2.61715	+	1.30318i
$10$		0			0
$11$	−1.95756	−	0.181395i	−1.95756	−	0.181395i	−0.961826	−	0.273663i	$-0.911765\pi$
$11$	−1.95756	−	0.181395i	−1.95756	−	0.181395i	−0.995734	+	0.0922684i	$0.970588\pi$
$12$	−1.96183	+	0.273663i	−1.96183	+	0.273663i
$13$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$13$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$14$		0			0
$15$		0			0
$16$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$17$	0.293271	+	0.221468i	0.293271	+	0.221468i	0.739009	−	0.673696i	$-0.235294\pi$
$17$	0.293271	+	0.221468i	0.293271	+	0.221468i	−0.445738	+	0.895163i	$0.647059\pi$
$18$	2.72622	+	1.05614i	2.72622	+	1.05614i
$19$	−0.576554	+	1.48826i	−0.576554	+	1.48826i	0.273663	+	0.961826i	$0.411765\pi$
$19$	−0.576554	+	1.48826i	−0.576554	+	1.48826i	−0.850217	+	0.526432i	$0.823529\pi$
$20$		0			0
$21$		0			0
$22$	1.18475	+	1.56886i	1.18475	+	1.56886i
$23$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$23$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$24$	1.52391	+	1.26544i	1.52391	+	1.26544i
$25$	0.995734	−	0.0922684i	0.995734	−	0.0922684i
$26$		0			0
$27$	−2.43427	−	2.93148i	−2.43427	−	2.93148i
$28$		0			0
$29$		0			0		0.824997	−	0.565136i	$-0.191176\pi$
$29$		0			0		−0.824997	+	0.565136i	$0.808824\pi$
$30$		0			0
$31$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$31$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$32$	0.526432	+	0.850217i	0.526432	+	0.850217i
$33$	−0.538007	−	3.85684i	−0.538007	−	3.85684i
$34$	−0.0339085	−	0.365931i	−0.0339085	−	0.365931i
$35$		0			0
$36$	−1.05614	−	2.72622i	−1.05614	−	2.72622i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	1.48826	−	0.576554i	1.48826	−	0.576554i
$39$		0			0
$40$		0			0
$41$	−0.323785	+	0.323785i	−0.323785	+	0.323785i	−0.850217	−	0.526432i	$-0.823529\pi$
$41$	−0.323785	+	0.323785i	−0.323785	+	0.323785i	0.526432	+	0.850217i	$0.323529\pi$
$42$		0			0
$43$	0.456541	+	1.03397i	0.456541	+	1.03397i	0.982973	+	0.183750i	$0.0588235\pi$
$43$	0.456541	+	1.03397i	0.456541	+	1.03397i	−0.526432	+	0.850217i	$0.676471\pi$
$44$	0.361242	−	1.93247i	0.361242	−	1.93247i
$45$		0			0
$46$		0			0
$47$		0			0		−0.948161	−	0.317791i	$-0.897059\pi$
$47$		0			0		0.948161	+	0.317791i	$0.102941\pi$
$48$	−0.0914812	−	1.97871i	−0.0914812	−	1.97871i
$49$	0.850217	−	0.526432i	0.850217	−	0.526432i
$50$	−0.739009	−	0.673696i	−0.739009	−	0.673696i
$51$	−0.294034	+	0.665924i	−0.294034	+	0.665924i
$52$		0			0
$53$		0			0		0.914794	−	0.403921i	$-0.132353\pi$
$53$		0			0		−0.914794	+	0.403921i	$0.867647\pi$
$54$	−0.526432	+	3.77387i	−0.526432	+	3.77387i
$55$		0			0
$56$		0			0
$57$	−3.13114	−	0.436776i	−3.13114	−	0.436776i
$58$		0			0
$59$	0.658809	+	1.32307i	0.658809	+	1.32307i	0.932472	+	0.361242i	$0.117647\pi$
$59$	0.658809	+	1.32307i	0.658809	+	1.32307i	−0.273663	+	0.961826i	$0.588235\pi$
$60$		0			0
$61$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$61$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$62$		0			0
$63$		0			0
$64$	0.273663	−	0.961826i	0.273663	−	0.961826i
$65$		0			0
$66$	−2.48779	+	2.99593i	−2.48779	+	2.99593i
$67$	0.241393	+	0.134455i	0.241393	+	0.134455i	0.602635	−	0.798017i	$-0.294118\pi$
$67$	0.241393	+	0.134455i	0.241393	+	0.134455i	−0.361242	+	0.932472i	$0.617647\pi$
$68$	−0.247582	+	0.271585i	−0.247582	+	0.271585i
$69$		0			0
$70$		0			0
$71$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$71$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$72$	−1.30318	+	2.61715i	−1.30318	+	2.61715i
$73$	−0.288130	+	1.01267i	−0.288130	+	1.01267i	0.673696	+	0.739009i	$0.264706\pi$
$73$	−0.288130	+	1.01267i	−0.288130	+	1.01267i	−0.961826	+	0.273663i	$0.911765\pi$
$74$		0			0
$75$	0.629488	+	1.87814i	0.629488	+	1.87814i
$76$	−1.42871	−	0.711414i	−1.42871	−	0.711414i
$77$		0			0
$78$		0			0
$79$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$79$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$80$		0			0
$81$	2.78663	−	3.69010i	2.78663	−	3.69010i
$82$	0.457413	+	0.0211475i	0.457413	+	0.0211475i
$83$	0.134455	−	0.963876i	0.134455	−	0.963876i	−0.798017	−	0.602635i	$-0.794118\pi$
$83$	0.134455	−	0.963876i	0.134455	−	0.963876i	0.932472	−	0.361242i	$-0.117647\pi$
$84$		0			0
$85$		0			0
$86$	0.456541	−	1.03397i	0.456541	−	1.03397i
$87$		0			0
$88$	−1.67148	+	1.03494i	−1.67148	+	1.03494i
$89$	−0.0373089	−	0.806980i	−0.0373089	−	0.806980i	−0.932472	−	0.361242i	$-0.882353\pi$
$89$	−0.0373089	−	0.806980i	−0.0373089	−	0.806980i	0.895163	−	0.445738i	$-0.147059\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.40065	+	1.40065i	−1.40065	+	1.40065i
$97$	−1.18375	+	0.982973i	−1.18375	+	0.982973i	−0.183750	+	0.982973i	$0.558824\pi$
$97$	−1.18375	+	0.982973i	−1.18375	+	0.982973i	−1.00000			$\pi$
$98$	−0.961826	−	0.273663i	−0.961826	−	0.273663i
$99$	5.35961	−	2.07632i	5.35961	−	2.07632i
$100$			1.00000i			1.00000i
$101$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$101$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$102$	0.690213	−	0.231336i	0.690213	−	0.231336i
$103$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$103$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.288130	−	0.465346i	0.288130	−	0.465346i	−0.673696	−	0.739009i	$-0.735294\pi$
$107$	0.288130	−	0.465346i	0.288130	−	0.465346i	0.961826	+	0.273663i	$0.0882353\pi$
$108$	3.14358	−	2.15340i	3.14358	−	2.15340i
$109$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$109$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.49780	+	1.24376i	1.49780	+	1.24376i	0.895163	+	0.445738i	$0.147059\pi$
$113$	1.49780	+	1.24376i	1.49780	+	1.24376i	0.602635	+	0.798017i	$0.294118\pi$
$114$	1.78666	+	2.60820i	1.78666	+	2.60820i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.533922	−	1.37821i	0.533922	−	1.37821i
$119$		0			0
$120$		0			0
$121$	2.81616	+	0.526432i	2.81616	+	0.526432i
$122$		0			0
$123$	−0.771164	−	0.477485i	−0.771164	−	0.477485i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$127$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$128$	−0.895163	+	0.445738i	−0.895163	+	0.445738i
$129$	−1.78666	+	1.34922i	−1.78666	+	1.34922i
$130$		0			0
$131$	−0.932472	+	1.36124i	−0.932472	+	1.36124i			1.00000i	$0.5\pi$
$131$	−0.932472	+	1.36124i	−0.932472	+	1.36124i	−0.932472	+	0.361242i	$0.882353\pi$
$132$	3.89003	−	0.179847i	3.89003	−	0.179847i
$133$		0			0
$134$	−0.0632619	−	0.268973i	−0.0632619	−	0.268973i
$135$		0			0
$136$	0.367499			0.367499
$137$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$137$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$138$		0			0
$139$	0.811985	+	0.890705i	0.811985	+	0.890705i	0.995734	−	0.0922684i	$-0.0294118\pi$
$139$	0.811985	+	0.890705i	0.811985	+	0.890705i	−0.183750	+	0.982973i	$0.558824\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.81204	−	0.800095i	2.81204	−	0.800095i
$145$		0			0
$146$	0.942485	−	0.469302i	0.942485	−	0.469302i
$147$	1.40065	+	1.40065i	1.40065	+	1.40065i
$148$		0			0
$149$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$149$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$150$	0.963876	−	1.73049i	0.963876	−	1.73049i
$151$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$151$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$152$	0.436776	+	1.53511i	0.436776	+	1.53511i
$153$	−1.05614	−	0.197428i	−1.05614	−	0.197428i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$157$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−4.60436	+	0.426657i	−4.60436	+	0.426657i
$163$	1.24376	−	0.292529i	1.24376	−	0.292529i	0.445738	−	0.895163i	$-0.352941\pi$
$163$	1.24376	−	0.292529i	1.24376	−	0.292529i	0.798017	+	0.602635i	$0.205882\pi$
$164$	−0.292529	−	0.352279i	−0.292529	−	0.352279i
$165$		0			0
$166$	−0.802895	+	0.549996i	−0.802895	+	0.549996i
$167$		0			0		0.526432	−	0.850217i	$-0.323529\pi$
$167$		0			0		−0.526432	+	0.850217i	$0.676471\pi$
$168$		0			0
$169$	−0.526432	−	0.850217i	−0.526432	−	0.850217i
$170$		0			0
$171$	−0.430547	−	4.64634i	−0.430547	−	4.64634i
$172$	−1.07168	+	0.359191i	−1.07168	+	0.359191i
$173$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$173$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$174$		0			0
$175$		0			0
$176$	1.89090	+	0.538007i	1.89090	+	0.538007i
$177$	−2.25237	+	1.87034i	−2.25237	+	1.87034i
$178$	−0.571231	+	0.571231i	−0.571231	+	0.571231i
$179$	0.618701	−	1.84595i	0.618701	−	1.84595i	0.0922684	−	0.995734i	$-0.470588\pi$
$179$	0.618701	−	1.84595i	0.618701	−	1.84595i	0.526432	−	0.850217i	$-0.323529\pi$
$180$		0			0
$181$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$181$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.533922	−	0.486734i	−0.533922	−	0.486734i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$191$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$192$	1.97871	+	0.0914812i	1.97871	+	0.0914812i
$193$	−1.20013	+	1.58923i	−1.20013	+	1.58923i	−0.526432	+	0.850217i	$0.676471\pi$
$193$	−1.20013	+	1.58923i	−1.20013	+	1.58923i	−0.673696	+	0.739009i	$0.735294\pi$
$194$	1.52391	+	0.212577i	1.52391	+	0.212577i
$195$		0			0
$196$	0.445738	+	0.895163i	0.445738	+	0.895163i
$197$		0			0		0.982973	−	0.183750i	$-0.0588235\pi$
$197$		0			0		−0.982973	+	0.183750i	$0.941176\pi$
$198$	−5.14517	−	2.56199i	−5.14517	−	2.56199i
$199$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$199$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$200$	0.739009	−	0.673696i	0.739009	−	0.673696i
$201$	−0.149783	+	0.526432i	−0.149783	+	0.526432i
$202$		0			0
$203$		0			0
$204$	−0.635953	−	0.354224i	−0.635953	−	0.354224i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.39860	−	2.80877i	1.39860	−	2.80877i
$210$		0			0
$211$	0.995734	−	0.907732i	0.995734	−	0.907732i		−	1.00000i	$-0.5\pi$
$211$	0.995734	−	0.907732i	0.995734	−	0.907732i	0.995734	+	0.0922684i	$0.0294118\pi$
$212$		0			0
$213$		0			0
$214$	−0.538007	+	0.100571i	−0.538007	+	0.100571i
$215$		0			0
$216$	−3.70920	−	0.872395i	−3.70920	−	0.872395i
$217$		0			0
$218$		0			0
$219$	−2.08331	−	0.0963172i	−2.08331	−	0.0963172i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$223$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$224$		0			0
$225$	−2.48574	+	1.53910i	−2.48574	+	1.53910i
$226$	−0.0899135	−	1.94480i	−0.0899135	−	1.94480i
$227$	−0.922758	−	0.309277i	−0.922758	−	0.309277i	−0.183750	−	0.982973i	$-0.558824\pi$
$227$	−0.922758	−	0.309277i	−0.922758	−	0.309277i	−0.739009	+	0.673696i	$0.764706\pi$
$228$	0.723818	−	3.07748i	0.723818	−	3.07748i
$229$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$229$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.903466	+	0.903466i	−0.903466	+	0.903466i	−0.995734	−	0.0922684i	$-0.970588\pi$
$233$	−0.903466	+	0.903466i	−0.903466	+	0.903466i	0.0922684	+	0.995734i	$0.470588\pi$
$234$		0			0
$235$		0			0
$236$	−1.37821	+	0.533922i	−1.37821	+	0.533922i
$237$		0			0
$238$		0			0
$239$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$239$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$240$		0			0
$241$	−0.212577	−	1.52391i	−0.212577	−	1.52391i	−0.739009	−	0.673696i	$-0.764706\pi$
$241$	−0.212577	−	1.52391i	−0.212577	−	1.52391i	0.526432	−	0.850217i	$-0.323529\pi$
$242$	−1.50820	−	2.43582i	−1.50820	−	2.43582i
$243$	4.89330	+	2.16060i	4.89330	+	2.16060i
$244$		0			0
$245$		0			0
$246$	0.166664	+	0.891576i	0.166664	+	0.891576i
$247$		0			0
$248$		0			0
$249$	1.91953	−	0.177871i	1.91953	−	0.177871i
$250$		0			0
$251$	0.932472	+	1.36124i	0.932472	+	1.36124i	0.932472	+	0.361242i	$0.117647\pi$
$251$	0.932472	+	1.36124i	0.932472	+	1.36124i			1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.932472	+	0.361242i	0.932472	+	0.361242i
$257$	1.35698	+	1.02474i	1.35698	+	1.02474i	0.995734	+	0.0922684i	$0.0294118\pi$
$257$	1.35698	+	1.02474i	1.35698	+	1.02474i	0.361242	+	0.932472i	$0.382353\pi$
$258$	2.20075	+	0.411391i	2.20075	+	0.411391i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.63417	−	0.227957i	1.63417	−	0.227957i
$263$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$263$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$264$	−2.75361	−	2.75361i	−2.75361	−	2.75361i
$265$		0			0
$266$		0			0
$267$	1.53910	−	0.437913i	1.53910	−	0.437913i
$268$	−0.156154	+	0.227957i	−0.156154	+	0.227957i
$269$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$269$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$270$		0			0
$271$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$271$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$272$	−0.247582	−	0.271585i	−0.247582	−	0.271585i
$273$		0			0
$274$	−0.445738	+	0.895163i	−0.445738	+	0.895163i
$275$	−1.96595			−1.96595
$276$		0			0
$277$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$277$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$278$	0.111208	−	1.20013i	0.111208	−	1.20013i
$279$		0			0
$280$		0			0
$281$	1.15926	−	0.329838i	1.15926	−	0.329838i	0.361242	−	0.932472i	$-0.382353\pi$
$281$	1.15926	−	0.329838i	1.15926	−	0.329838i	0.798017	+	0.602635i	$0.205882\pi$
$282$		0			0
$283$	−1.60263	+	0.798017i	−1.60263	+	0.798017i	−0.602635	+	0.798017i	$0.705882\pi$
$283$	−1.60263	+	0.798017i	−1.60263	+	0.798017i	−1.00000			$1.00000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.48574	−	1.53910i	−2.48574	−	1.53910i
$289$	−0.236703	−	0.831926i	−0.236703	−	0.831926i
$290$		0			0
$291$	−2.43222	−	1.83673i	−2.43222	−	1.83673i
$292$	−0.981767	−	0.380338i	−0.981767	−	0.380338i
$293$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$293$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$294$	0.0914812	−	1.97871i	0.0914812	−	1.97871i
$295$		0			0
$296$		0			0
$297$	4.23347	+	6.18010i	4.23347	+	6.18010i
$298$		0			0
$299$		0			0
$300$	−1.92821	+	0.453510i	−1.92821	+	0.453510i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.840204	−	1.35698i	0.840204	−	1.35698i
$305$		0			0
$306$	0.565619	+	0.913506i	0.565619	+	0.913506i
$307$	0.0381744	+	0.273663i	0.0381744	+	0.273663i	1.00000			$0$
$307$	0.0381744	+	0.273663i	0.0381744	+	0.273663i	−0.961826	+	0.273663i	$0.911765\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−0.694903	−	0.197717i	−0.694903	−	0.197717i	−0.0922684	−	0.995734i	$-0.529412\pi$
$313$	−0.694903	−	0.197717i	−0.694903	−	0.197717i	−0.602635	+	0.798017i	$0.705882\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$317$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.02795	+	0.344535i	1.02795	+	0.344535i
$322$		0			0
$323$	−0.498687	+	0.308774i	−0.498687	+	0.308774i
$324$	3.41724	+	3.11523i	3.41724	+	3.11523i
$325$		0			0
$326$	−1.05409	−	0.722071i	−1.05409	−	0.722071i
$327$		0			0
$328$	−0.0632619	+	0.453510i	−0.0632619	+	0.453510i
$329$		0			0
$330$		0			0
$331$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.798017	−	0.602635i	$-0.205882\pi$
$331$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.602635	+	0.798017i	$0.294118\pi$
$332$	0.947359	+	0.222817i	0.947359	+	0.222817i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.778076	−	0.709310i	0.778076	−	0.709310i	−0.183750	−	0.982973i	$-0.558824\pi$
$337$	0.778076	−	0.709310i	0.778076	−	0.709310i	0.961826	+	0.273663i	$0.0882353\pi$
$338$	−0.273663	+	0.961826i	−0.273663	+	0.961826i
$339$	−1.71895	+	3.45212i	−1.71895	+	3.45212i
$340$		0			0
$341$		0			0
$342$	−3.14363	+	3.44840i	−3.14363	+	3.44840i
$343$		0			0
$344$	0.987432	+	0.549996i	0.987432	+	0.549996i
$345$		0			0
$346$		0			0
$347$	0.243964	−	0.857445i	0.243964	−	0.857445i	−0.739009	−	0.673696i	$-0.764706\pi$
$347$	0.243964	−	0.857445i	0.243964	−	0.857445i	0.982973	−	0.183750i	$-0.0588235\pi$
$348$		0			0
$349$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$349$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$350$		0			0
$351$		0			0
$352$	−0.876298	−	1.75984i	−0.876298	−	1.75984i
$353$	1.70083	+	0.400033i	1.70083	+	0.400033i	0.961826	−	0.273663i	$-0.0882353\pi$
$353$	1.70083	+	0.400033i	1.70083	+	0.400033i	0.739009	+	0.673696i	$0.235294\pi$
$354$	2.89961	+	0.404479i	2.89961	+	0.404479i
$355$		0			0
$356$	0.806980	+	0.0373089i	0.806980	+	0.0373089i
$357$		0			0
$358$	−1.78099	+	0.786384i	−1.78099	+	0.786384i
$359$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$359$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$360$		0			0
$361$	−1.14349	−	1.04243i	−1.14349	−	1.04243i
$362$		0			0
$363$	0.262088	+	5.66889i	0.262088	+	5.66889i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$367$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$368$		0			0
$369$	0.425441	−	1.26934i	0.425441	−	1.26934i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$373$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$374$			0.722483i			0.722483i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.0971461	−	0.156896i	−0.0971461	−	0.156896i	0.798017	−	0.602635i	$-0.205882\pi$
$379$	−0.0971461	−	0.156896i	−0.0971461	−	0.156896i	−0.895163	+	0.445738i	$0.852941\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$383$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$384$	−1.26544	−	1.52391i	−1.26544	−	1.52391i
$385$		0			0
$386$	1.98297	−	0.183750i	1.98297	−	0.183750i
$387$	−2.54228	−	2.11108i	−2.54228	−	2.11108i
$388$	−0.869557	−	1.26940i	−0.869557	−	1.26940i
$389$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$389$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$390$		0			0
$391$		0			0
$392$	0.361242	−	0.932472i	0.361242	−	0.932472i
$393$	−3.04764	−	1.18066i	−3.04764	−	1.18066i
$394$		0			0
$395$		0			0
$396$	1.57294	+	5.52832i	1.57294	+	5.52832i
$397$		0			0		−0.850217	−	0.526432i	$-0.823529\pi$
$397$		0			0		0.850217	+	0.526432i	$0.176471\pi$
$398$		0			0
$399$		0			0
$400$	−0.995734	−	0.0922684i	−0.995734	−	0.0922684i
$401$	0.449425	+	0.449425i	0.449425	+	0.449425i	0.895163	−	0.445738i	$-0.147059\pi$
$401$	0.449425	+	0.449425i	0.449425	+	0.449425i	−0.445738	+	0.895163i	$0.647059\pi$
$402$	0.489946	−	0.243964i	0.489946	−	0.243964i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.166664	+	0.708614i	0.166664	+	0.708614i
$409$	−0.124322	−	0.136374i	−0.124322	−	0.136374i	0.673696	−	0.739009i	$-0.264706\pi$
$409$	−0.124322	−	0.136374i	−0.124322	−	0.136374i	−0.798017	+	0.602635i	$0.794118\pi$
$410$		0			0
$411$	1.63417	−	1.11943i	1.63417	−	1.11943i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.34922	+	1.96962i	−1.34922	+	1.96962i
$418$	−3.01794	+	0.858677i	−3.01794	+	0.858677i
$419$	0.147263	−	0.111208i	0.147263	−	0.111208i	−0.526432	−	0.850217i	$-0.676471\pi$
$419$	0.147263	−	0.111208i	0.147263	−	0.111208i	0.673696	+	0.739009i	$0.264706\pi$
$420$		0			0
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	−1.34164	−	0.124322i	−1.34164	−	0.124322i
$423$		0			0
$424$		0			0
$425$	0.312454	+	0.193463i	0.312454	+	0.193463i
$426$		0			0
$427$		0			0
$428$	0.436776	+	0.329838i	0.436776	+	0.329838i
$429$		0			0
$430$		0			0
$431$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$431$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$432$	1.85416	+	3.32886i	1.85416	+	3.32886i
$433$	−1.20013	−	1.58923i	−1.20013	−	1.58923i	−0.673696	−	0.739009i	$-0.735294\pi$
$433$	−1.20013	−	1.58923i	−1.20013	−	1.58923i	−0.526432	−	0.850217i	$-0.676471\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.33234	+	1.60447i	1.33234	+	1.60447i
$439$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$439$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$440$		0			0
$441$	−1.53910	+	2.48574i	−1.53910	+	2.48574i
$442$		0			0
$443$	−1.04837	−	1.69318i	−1.04837	−	1.69318i	−0.602635	−	0.798017i	$-0.705882\pi$
$443$	−1.04837	−	1.69318i	−1.04837	−	1.69318i	−0.445738	−	0.895163i	$-0.647059\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	−0.273663	−	0.961826i	$-0.588235\pi$
$449$	0.172075	−	0.0666624i	0.172075	−	0.0666624i	0.445738	+	0.895163i	$0.352941\pi$
$450$	2.81204	+	0.800095i	2.81204	+	0.800095i
$451$	0.692561	−	0.575096i	0.692561	−	0.575096i
$452$	−1.37665	+	1.37665i	−1.37665	+	1.37665i
$453$		0			0
$454$	0.393100	+	0.890286i	0.393100	+	0.890286i
$455$		0			0
$456$	−2.76192	+	1.53838i	−2.76192	+	1.53838i
$457$	0.258777	−	1.10025i	0.258777	−	1.10025i	−0.673696	−	0.739009i	$-0.735294\pi$
$457$	0.258777	−	1.10025i	0.258777	−	1.10025i	0.932472	−	0.361242i	$-0.117647\pi$
$458$		0			0
$459$	−0.0646717	−	1.39883i	−0.0646717	−	1.39883i
$460$		0			0
$461$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$461$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$462$		0			0
$463$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$463$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$464$		0			0
$465$		0			0
$466$	1.27633	+	0.0590083i	1.27633	+	0.0590083i
$467$	−1.02474	+	1.35698i	−1.02474	+	1.35698i	−0.0922684	+	0.995734i	$0.529412\pi$
$467$	−1.02474	+	1.35698i	−1.02474	+	1.35698i	−0.932472	+	0.361242i	$0.882353\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.32307	+	0.658809i	1.32307	+	0.658809i
$473$	−0.706150	−	2.10687i	−0.706150	−	2.10687i
$474$		0			0
$475$	−0.436776	+	1.53511i	−0.436776	+	1.53511i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$479$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$480$		0			0
$481$		0			0
$482$	−0.982973	+	1.18375i	−0.982973	+	1.18375i
$483$		0			0
$484$	−0.784029	+	2.75558i	−0.784029	+	2.75558i
$485$		0			0
$486$	−1.69989	−	5.07178i	−1.69989	−	5.07178i
$487$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$487$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$488$		0			0
$489$	1.12811	+	2.26555i	1.12811	+	2.26555i
$490$		0			0
$491$	0.0914812	+	0.0127611i	0.0914812	+	0.0127611i	0.183750	−	0.982973i	$-0.441176\pi$
$491$	0.0914812	+	0.0127611i	0.0914812	+	0.0127611i	−0.0922684	+	0.995734i	$0.529412\pi$
$492$	0.546602	−	0.723818i	0.546602	−	0.723818i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.42463	−	1.29872i	−1.42463	−	1.29872i
$499$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	−0.850217	−	0.526432i	$-0.823529\pi$
$499$	−0.757949	+	0.469302i	−0.757949	+	0.469302i	0.0922684	+	0.995734i	$0.470588\pi$
$500$		0			0
$501$		0			0
$502$	0.377767	−	1.60617i	0.377767	−	1.60617i
$503$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$503$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.40065	−	1.40065i	1.40065	−	1.40065i
$508$		0			0
$509$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$509$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$510$		0			0
$511$		0			0
$512$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$513$	5.76628	−	1.93266i	5.76628	−	1.93266i
$514$	−0.156896	−	1.69318i	−0.156896	−	1.69318i
$515$		0			0
$516$	−1.17861	−	1.90352i	−1.17861	−	1.90352i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.292529	−	0.352279i	−0.292529	−	0.352279i	0.602635	−	0.798017i	$-0.294118\pi$
$521$	−0.292529	−	0.352279i	−0.292529	−	0.352279i	−0.895163	+	0.445738i	$0.852941\pi$
$522$		0			0
$523$	0.887674	−	0.0822551i	0.887674	−	0.0822551i	0.361242	−	0.932472i	$-0.382353\pi$
$523$	0.887674	−	0.0822551i	0.887674	−	0.0822551i	0.526432	+	0.850217i	$0.323529\pi$
$524$	−1.26940	−	1.05409i	−1.26940	−	1.05409i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.179847	+	3.89003i	−0.179847	+	3.89003i
$529$	−0.361242	+	0.932472i	−0.361242	+	0.932472i
$530$		0			0
$531$	−3.44840	−	2.60411i	−3.44840	−	2.60411i
$532$		0			0
$533$		0			0
$534$	−1.36051	−	0.842392i	−1.36051	−	0.842392i
$535$		0			0
$536$	0.273663	−	0.0381744i	0.273663	−	0.0381744i
$537$	3.83996	+	0.355825i	3.83996	+	0.355825i
$538$		0			0
$539$	−1.75984	+	0.876298i	−1.75984	+	0.876298i
$540$		0			0
$541$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$541$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$542$		0			0
$543$		0			0
$544$	−0.0339085	+	0.365931i	−0.0339085	+	0.365931i
$545$		0			0
$546$		0			0
$547$	1.70043			1.70043			0.850217	−	0.526432i	$-0.176471\pi$
$547$	1.70043			1.70043			0.850217	+	0.526432i	$0.176471\pi$
$548$	0.961826	−	0.273663i	0.961826	−	0.273663i
$549$		0			0
$550$	1.32445	+	1.45285i	1.32445	+	1.45285i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.961826	+	0.726337i	−0.961826	+	0.726337i
$557$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$557$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.696385	−	1.25025i	0.696385	−	1.25025i
$562$	−1.02474	−	0.634493i	−1.02474	−	0.634493i
$563$	−0.149783	−	0.526432i	−0.149783	−	0.526432i	0.850217	−	0.526432i	$-0.176471\pi$
$563$	−0.149783	−	0.526432i	−0.149783	−	0.526432i	−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	1.66943	+	0.646741i	1.66943	+	0.646741i
$567$		0			0
$568$		0			0
$569$	0.922758	+	1.65667i	0.922758	+	1.65667i	0.739009	+	0.673696i	$0.235294\pi$
$569$	0.922758	+	1.65667i	0.922758	+	1.65667i	0.183750	+	0.982973i	$0.441176\pi$
$570$		0			0
$571$	−0.987432	−	1.44147i	−0.987432	−	1.44147i	−0.895163	−	0.445738i	$-0.852941\pi$
$571$	−0.987432	−	1.44147i	−0.987432	−	1.44147i	−0.0922684	−	0.995734i	$-0.529412\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.537220	+	2.87387i	0.537220	+	2.87387i
$577$	0.524354	−	0.359191i	0.524354	−	0.359191i	−0.273663	−	0.961826i	$-0.588235\pi$
$577$	0.524354	−	0.359191i	0.524354	−	0.359191i	0.798017	+	0.602635i	$0.205882\pi$
$578$	−0.455335	+	0.735391i	−0.455335	+	0.735391i
$579$	−3.60863	−	1.59336i	−3.60863	−	1.59336i
$580$		0			0
$581$		0			0
$582$	0.281218	+	3.03482i	0.281218	+	3.03482i
$583$		0			0
$584$	0.380338	+	0.981767i	0.380338	+	0.981767i
$585$		0			0
$586$		0			0
$587$	−1.79375	−	0.510366i	−1.79375	−	0.510366i	−0.798017	−	0.602635i	$-0.794118\pi$
$587$	−1.79375	−	0.510366i	−1.79375	−	0.510366i	−0.995734	+	0.0922684i	$0.970588\pi$
$588$	−1.52391	+	1.26544i	−1.52391	+	1.26544i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.74538	+	0.972171i	−1.74538	+	0.972171i	−0.850217	+	0.526432i	$0.823529\pi$
$593$	−1.74538	+	0.972171i	−1.74538	+	0.972171i	−0.895163	+	0.445738i	$0.852941\pi$
$594$	1.71508	−	7.29208i	1.71508	−	7.29208i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.403921	−	0.914794i	$-0.367647\pi$
$599$		0			0		−0.403921	+	0.914794i	$0.632353\pi$
$600$	1.63417	+	1.11943i	1.63417	+	1.11943i
$601$	1.59837	−	0.705749i	1.59837	−	0.705749i	0.602635	−	0.798017i	$-0.294118\pi$
$601$	1.59837	−	0.705749i	1.59837	−	0.705749i	0.995734	+	0.0922684i	$0.0294118\pi$
$602$		0			0
$603$	−0.806980	−	0.0373089i	−0.806980	−	0.0373089i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.445738	−	0.895163i	$-0.647059\pi$
$607$		0			0		0.445738	+	0.895163i	$0.352941\pi$
$608$	−1.56886	+	0.293271i	−1.56886	+	0.293271i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.294034	−	1.03342i	0.294034	−	1.03342i
$613$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$613$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$614$	0.176521	−	0.212577i	0.176521	−	0.212577i
$615$		0			0
$616$		0			0
$617$	−0.486734	+	0.533922i	−0.486734	+	0.533922i	−0.932472	−	0.361242i	$-0.882353\pi$
$617$	−0.486734	+	0.533922i	−0.486734	+	0.533922i	0.445738	+	0.895163i	$0.352941\pi$
$618$		0			0
$619$	−0.406040	+	0.488975i	−0.406040	+	0.488975i	−0.932472	−	0.361242i	$-0.882353\pi$
$619$	−0.406040	+	0.488975i	−0.406040	+	0.488975i	0.526432	+	0.850217i	$0.323529\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.982973	−	0.183750i	0.982973	−	0.183750i
$626$	0.322039	+	0.646741i	0.322039	+	0.646741i
$627$	6.05017	+	1.42299i	6.05017	+	1.42299i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$631$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$632$		0			0
$633$	2.20187	+	1.50832i	2.20187	+	1.50832i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.328972	+	1.75984i	−0.328972	+	1.75984i	0.273663	+	0.961826i	$0.411765\pi$
$641$	−0.328972	+	1.75984i	−0.328972	+	1.75984i	−0.602635	+	0.798017i	$0.705882\pi$
$642$	−0.437913	−	0.991778i	−0.437913	−	0.991778i
$643$	0.602635	−	1.79802i	0.602635	−	1.79802i		−	1.00000i	$-0.5\pi$
$643$	0.602635	−	1.79802i	0.602635	−	1.79802i	0.602635	−	0.798017i	$-0.294118\pi$
$644$		0			0
$645$		0			0
$646$	0.564150	+	0.160515i	0.564150	+	0.160515i
$647$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$647$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$648$		−	4.62409i		−	4.62409i
$649$	−1.04966	−	2.70949i	−1.04966	−	2.70949i
$650$		0			0
$651$		0			0
$652$	0.176521	+	1.26544i	0.176521	+	1.26544i
$653$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$653$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$654$		0			0
$655$		0			0
$656$	0.377767	−	0.258777i	0.377767	−	0.258777i
$657$	−0.565619	−	3.02580i	−0.565619	−	3.02580i
$658$		0			0
$659$	−1.70083	+	0.400033i	−1.70083	+	0.400033i	−0.961826	−	0.273663i	$-0.911765\pi$
$659$	−1.70083	+	0.400033i	−1.70083	+	0.400033i	−0.739009	+	0.673696i	$0.764706\pi$
$660$		0			0
$661$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$661$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$662$	−0.799224	−	1.16672i	−0.799224	−	1.16672i
$663$		0			0
$664$	−0.473568	−	0.850217i	−0.473568	−	0.850217i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.63417	+	0.227957i	−1.63417	+	0.227957i	−0.895163	−	0.445738i	$-0.852941\pi$
$673$	−1.63417	+	0.227957i	−1.63417	+	0.227957i	−0.739009	+	0.673696i	$0.764706\pi$
$674$	−1.04837	−	0.0971461i	−1.04837	−	0.0971461i
$675$	−2.69437	−	2.69437i	−2.69437	−	2.69437i
$676$	0.895163	−	0.445738i	0.895163	−	0.445738i
$677$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$677$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$678$	3.70920	−	1.05536i	3.70920	−	1.05536i
$679$		0			0
$680$		0			0
$681$	0.177871	−	1.91953i	0.177871	−	1.91953i
$682$		0			0
$683$	−0.709310	−	0.778076i	−0.709310	−	0.778076i	0.273663	−	0.961826i	$-0.411765\pi$
$683$	−0.709310	−	0.778076i	−0.709310	−	0.778076i	−0.982973	+	0.183750i	$0.941176\pi$
$684$	4.66625			4.66625
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.258777	−	1.10025i	−0.258777	−	1.10025i
$689$		0			0
$690$		0			0
$691$	0.799224	−	1.16672i	0.799224	−	1.16672i	−0.183750	−	0.982973i	$-0.558824\pi$
$691$	0.799224	−	1.16672i	0.799224	−	1.16672i	0.982973	−	0.183750i	$-0.0588235\pi$
$692$		0			0
$693$		0			0
$694$	−0.798017	+	0.397365i	−0.798017	+	0.397365i
$695$		0			0
$696$		0			0
$697$	−0.166664	+	0.0232487i	−0.166664	+	0.0232487i
$698$		0			0
$699$	−2.15180	−	1.33234i	−2.15180	−	1.33234i
$700$		0			0
$701$		0			0		−0.982973	−	0.183750i	$-0.941176\pi$
$701$		0			0		0.982973	+	0.183750i	$0.0588235\pi$
$702$		0			0
$703$		0			0
$704$	−0.710182	+	1.83319i	−0.710182	+	1.83319i
$705$		0			0
$706$	−0.850217	−	1.52643i	−0.850217	−	1.52643i
$707$		0			0
$708$	−1.65454	−	2.41534i	−1.65454	−	2.41534i
$709$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$709$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$710$		0			0
$711$		0			0
$712$	−0.516087	−	0.621500i	−0.516087	−	0.621500i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.78099	+	0.786384i	1.78099	+	0.786384i
$717$		0			0
$718$		0			0
$719$		0			0		−0.0922684	−	0.995734i	$-0.529412\pi$
$719$		0			0		0.0922684	+	0.995734i	$0.470588\pi$
$720$		0			0
$721$		0			0
$722$			1.54733i			1.54733i
$723$	2.84201	−	1.10100i	2.84201	−	1.10100i
$724$		0			0
$725$		0			0
$726$	4.01279	−	4.01279i	4.01279	−	4.01279i
$727$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$727$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$728$		0			0
$729$	−1.09726	+	5.86980i	−1.09726	+	5.86980i
$730$		0			0
$731$	−0.0951001	+	0.404341i	−0.0951001	+	0.404341i
$732$		0			0
$733$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$733$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.448152	−	0.306991i	−0.448152	−	0.306991i
$738$	−1.22467	+	0.540746i	−1.22467	+	0.540746i
$739$	0.276018	−	1.97871i	0.276018	−	1.97871i	0.0922684	−	0.995734i	$-0.470588\pi$
$739$	0.276018	−	1.97871i	0.276018	−	1.97871i	0.183750	−	0.982973i	$-0.441176\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$743$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.904219	+	2.69782i	0.904219	+	2.69782i
$748$	0.533922	−	0.486734i	0.533922	−	0.486734i
$749$		0			0
$750$		0			0
$751$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$751$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$752$		0			0
$753$	−2.20187	+	2.41534i	−2.20187	+	2.41534i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$757$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$758$	−0.0505009	+	0.177492i	−0.0505009	+	0.177492i
$759$		0			0
$760$		0			0
$761$	−0.489946	−	0.243964i	−0.489946	−	0.243964i	0.183750	−	0.982973i	$-0.441176\pi$
$761$	−0.489946	−	0.243964i	−0.489946	−	0.243964i	−0.673696	+	0.739009i	$0.735294\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.273663	+	1.96183i	−0.273663	+	1.96183i
$769$	−0.0844967	+	0.0373089i	−0.0844967	+	0.0373089i	−0.445738	−	0.895163i	$-0.647059\pi$
$769$	−0.0844967	+	0.0373089i	−0.0844967	+	0.0373089i	0.361242	+	0.932472i	$0.382353\pi$
$770$		0			0
$771$	−1.36051	+	3.08126i	−1.36051	+	3.08126i
$772$	−1.47171	−	1.34164i	−1.47171	−	1.34164i
$773$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$773$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$774$	0.152614	+	3.30100i	0.152614	+	3.30100i
$775$		0			0
$776$	−0.352279	+	1.49780i	−0.352279	+	1.49780i
$777$		0			0
$778$		0			0
$779$	−0.295196	−	0.668555i	−0.295196	−	0.668555i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$785$		0			0
$786$	1.18066	+	3.04764i	1.18066	+	3.04764i
$787$	−1.21146	+	0.406040i	−1.21146	+	0.406040i	−0.850217	−	0.526432i	$-0.823529\pi$
$787$	−1.21146	+	0.406040i	−1.21146	+	0.406040i	−0.361242	+	0.932472i	$0.617647\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	3.02580	−	4.88683i	3.02580	−	4.88683i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$797$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$798$		0			0
$799$		0			0
$800$	0.602635	+	0.798017i	0.602635	+	0.798017i
$801$	1.14929	+	2.06336i	1.14929	+	2.06336i
$802$	0.0293534	−	0.634905i	0.0293534	−	0.634905i
$803$	0.747725	−	1.93010i	0.747725	−	1.93010i
$804$	−0.510366	−	0.197717i	−0.510366	−	0.197717i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0449462	−	0.0806938i	0.0449462	−	0.0806938i	−0.850217	−	0.526432i	$-0.823529\pi$
$809$	0.0449462	−	0.0806938i	0.0449462	−	0.0806938i	0.895163	+	0.445738i	$0.147059\pi$
$810$		0			0
$811$	1.34164	+	0.124322i	1.34164	+	0.124322i	0.739009	−	0.673696i	$-0.235294\pi$
$811$	1.34164	+	0.124322i	1.34164	+	0.124322i	0.602635	+	0.798017i	$0.294118\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.411391	−	0.600557i	0.411391	−	0.600557i
$817$	−1.80203	+	0.0833129i	−1.80203	+	0.0833129i
$818$	−0.0170269	+	0.183750i	−0.0170269	+	0.183750i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−1.92821	−	0.453510i	−1.92821	−	0.453510i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−0.891576	−	3.79075i	−0.891576	−	3.79075i
$826$		0			0
$827$	−0.457413	+	0.0211475i	−0.457413	+	0.0211475i	−0.273663	−	0.961826i	$-0.588235\pi$
$827$	−0.457413	+	0.0211475i	−0.457413	+	0.0211475i	−0.183750	+	0.982973i	$0.558824\pi$
$828$		0			0
$829$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$829$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.365931	+	0.0339085i	0.365931	+	0.0339085i
$834$	2.36453	−	0.329838i	2.36453	−	0.329838i
$835$		0			0
$836$	2.66774	+	1.65180i	2.66774	+	1.65180i
$837$		0			0
$838$	−0.181395	−	0.0339085i	−0.181395	−	0.0339085i
$839$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$839$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$840$		0			0
$841$	0.361242	−	0.932472i	0.361242	−	0.932472i
$842$		0			0
$843$	1.16173	+	2.08571i	1.16173	+	2.08571i
$844$	0.811985	+	1.07524i	0.811985	+	1.07524i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.26555	−	2.72830i	−2.26555	−	2.72830i
$850$	−0.0675278	−	0.361242i	−0.0675278	−	0.361242i
$851$		0			0
$852$		0			0
$853$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$853$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$854$		0			0
$855$		0			0
$856$	−0.0505009	−	0.544991i	−0.0505009	−	0.544991i
$857$	−0.261989	+	0.0878098i	−0.261989	+	0.0878098i	−0.445738	−	0.895163i	$-0.647059\pi$
$857$	−0.261989	+	0.0878098i	−0.261989	+	0.0878098i	0.183750	+	0.982973i	$0.441176\pi$
$858$		0			0
$859$		−	1.70043i		−	1.70043i	−0.526432	−	0.850217i	$-0.676471\pi$
$859$		−	1.70043i		−	1.70043i	0.526432	−	0.850217i	$-0.323529\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$	1.21092	−	3.61288i	1.21092	−	3.61288i
$865$		0			0
$866$	−0.365931	+	1.95756i	−0.365931	+	1.95756i
$867$	1.49678	−	0.833699i	1.49678	−	0.833699i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.81705	−	4.11523i	1.81705	−	4.11523i
$874$		0			0
$875$		0			0
$876$	0.288130	−	2.06554i	0.288130	−	2.06554i
$877$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$877$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.887674	+	1.78269i	0.887674	+	1.78269i	0.526432	+	0.850217i	$0.323529\pi$
$881$	0.887674	+	1.78269i	0.887674	+	1.78269i	0.361242	+	0.932472i	$0.382353\pi$
$882$	2.87387	−	0.537220i	2.87387	−	0.537220i
$883$	1.07891	+	0.537235i	1.07891	+	0.537235i	0.895163	−	0.445738i	$-0.147059\pi$
$883$	1.07891	+	0.537235i	1.07891	+	0.537235i	0.183750	+	0.982973i	$0.441176\pi$
$884$		0			0
$885$		0			0
$886$	−0.544991	+	1.91545i	−0.544991	+	1.91545i
$887$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$887$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6.12437	+	6.71811i	−6.12437	+	6.71811i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.165190	−	0.0822551i	−0.165190	−	0.0822551i
$899$		0			0
$900$	−1.30318	−	2.61715i	−1.30318	−	2.61715i
$901$		0			0
$902$	−0.891576	−	0.124370i	−0.891576	−	0.124370i
$903$		0			0
$904$	1.94480	+	0.0899135i	1.94480	+	0.0899135i
$905$		0			0
$906$		0			0
$907$	−1.44147	−	0.987432i	−1.44147	−	0.987432i	−0.995734	−	0.0922684i	$-0.970588\pi$
$907$	−1.44147	−	0.987432i	−1.44147	−	0.987432i	−0.445738	−	0.895163i	$-0.647059\pi$
$908$	0.393100	−	0.890286i	0.393100	−	0.890286i
$909$		0			0
$910$		0			0
$911$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$911$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$912$	2.99757	+	1.00468i	2.99757	+	1.00468i
$913$	−0.438046	+	1.86246i	−0.438046	+	1.86246i
$914$	−0.987432	+	0.549996i	−0.987432	+	0.549996i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.990177	+	0.990177i	−0.990177	+	0.990177i
$919$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$919$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$920$		0			0
$921$	−0.510366	+	0.197717i	−0.510366	+	0.197717i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.380338	−	0.614268i	0.380338	−	0.614268i	−0.602635	−	0.798017i	$-0.705882\pi$
$929$	0.380338	−	0.614268i	0.380338	−	0.614268i	0.982973	+	0.183750i	$0.0588235\pi$
$930$		0			0
$931$	0.293271	+	1.56886i	0.293271	+	1.56886i
$932$	−0.816250	−	0.982973i	−0.816250	−	0.982973i
$933$		0			0
$934$	1.69318	−	0.156896i	1.69318	−	0.156896i
$935$		0			0
$936$		0			0
$937$	1.07891	+	1.42871i	1.07891	+	1.42871i	0.895163	+	0.445738i	$0.147059\pi$
$937$	1.07891	+	1.42871i	1.07891	+	1.42871i	0.183750	+	0.982973i	$0.441176\pi$
$938$		0			0
$939$	0.0660936	−	1.42958i	0.0660936	−	1.42958i
$940$		0			0
$941$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$941$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$942$		0			0
$943$		0			0
$944$	−0.404479	−	1.42160i	−0.404479	−	1.42160i
$945$		0			0
$946$	−1.08126	+	1.94124i	−1.08126	+	1.94124i
$947$	1.97871	−	0.276018i	1.97871	−	0.276018i	0.982973	−	0.183750i	$-0.0588235\pi$
$947$	1.97871	−	0.276018i	1.97871	−	0.276018i	0.995734	−	0.0922684i	$-0.0294118\pi$
$948$		0			0
$949$		0			0
$950$	1.42871	−	0.711414i	1.42871	−	0.711414i
$951$		0			0
$952$		0			0
$953$	−1.03397	+	1.50941i	−1.03397	+	1.50941i	−0.183750	+	0.982973i	$0.558824\pi$
$953$	−1.03397	+	1.50941i	−1.03397	+	1.50941i	−0.850217	+	0.526432i	$0.823529\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.673696	+	0.739009i	0.673696	+	0.739009i
$962$		0			0
$963$	−0.147647	+	1.59336i	−0.147647	+	1.59336i
$964$	1.53703	−	0.0710610i	1.53703	−	0.0710610i
$965$		0			0
$966$		0			0
$967$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$967$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$968$	2.56459	−	1.27702i	2.56459	−	1.27702i
$969$	−0.821540	−	0.821540i	−0.821540	−	0.821540i
$970$		0			0
$971$	0.629488	−	0.0878098i	0.629488	−	0.0878098i	0.183750	−	0.982973i	$-0.441176\pi$
$971$	0.629488	−	0.0878098i	0.629488	−	0.0878098i	0.445738	+	0.895163i	$0.352941\pi$
$972$	−2.60288	+	4.67307i	−2.60288	+	4.67307i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$977$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$978$	0.914260	−	2.35998i	0.914260	−	2.35998i
$979$	−0.0733474	+	1.58648i	−0.0733474	+	1.58648i
$980$		0			0
$981$		0			0
$982$	−0.0521999	−	0.0762025i	−0.0521999	−	0.0762025i
$983$		0			0		−0.769334	−	0.638847i	$-0.779412\pi$
$983$		0			0		0.769334	+	0.638847i	$0.220588\pi$
$984$	−0.903151	+	0.0836893i	−0.903151	+	0.0836893i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$991$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$992$		0			0
$993$	0.258472	+	2.78935i	0.258472	+	2.78935i
$994$		0			0
$995$		0			0
$996$			1.92775i			1.92775i
$997$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$997$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$998$	0.857445	+	0.243964i	0.857445	+	0.243964i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.z.a.1027.1	yes	32
8.3	odd	2	CM	1096.1.z.a.1027.1	yes	32
137.135	even	68	inner	1096.1.z.a.683.1	✓	32
1096.683	odd	68	inner	1096.1.z.a.683.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.z.a.683.1	✓	32	137.135	even	68	inner
1096.1.z.a.683.1	✓	32	1096.683	odd	68	inner
1096.1.z.a.1027.1	yes	32	1.1	even	1	trivial
1096.1.z.a.1027.1	yes	32	8.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1096 = 2^{3} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1096.z (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.673696 - 0.739009i) q^{2} +(0.453510 + 1.92821i) q^{3} +(-0.0922684 + 0.995734i) q^{4} +(1.11943 - 1.63417i) q^{6} +(0.798017 - 0.602635i) q^{8} +(-2.61715 + 1.30318i) q^{9} +O(q^{10})\)	\(q+(-0.673696 - 0.739009i) q^{2} +(0.453510 + 1.92821i) q^{3} +(-0.0922684 + 0.995734i) q^{4} +(1.11943 - 1.63417i) q^{6} +(0.798017 - 0.602635i) q^{8} +(-2.61715 + 1.30318i) q^{9} +(-1.95756 - 0.181395i) q^{11} +(-1.96183 + 0.273663i) q^{12} +(-0.982973 - 0.183750i) q^{16} +(0.293271 + 0.221468i) q^{17} +(2.72622 + 1.05614i) q^{18} +(-0.576554 + 1.48826i) q^{19} +(1.18475 + 1.56886i) q^{22} +(1.52391 + 1.26544i) q^{24} +(0.995734 - 0.0922684i) q^{25} +(-2.43427 - 2.93148i) q^{27} +(0.526432 + 0.850217i) q^{32} +(-0.538007 - 3.85684i) q^{33} +(-0.0339085 - 0.365931i) q^{34} +(-1.05614 - 2.72622i) q^{36} +(1.48826 - 0.576554i) q^{38} +(-0.323785 + 0.323785i) q^{41} +(0.456541 + 1.03397i) q^{43} +(0.361242 - 1.93247i) q^{44} +(-0.0914812 - 1.97871i) q^{48} +(0.850217 - 0.526432i) q^{49} +(-0.739009 - 0.673696i) q^{50} +(-0.294034 + 0.665924i) q^{51} +(-0.526432 + 3.77387i) q^{54} +(-3.13114 - 0.436776i) q^{57} +(0.658809 + 1.32307i) q^{59} +(0.273663 - 0.961826i) q^{64} +(-2.48779 + 2.99593i) q^{66} +(0.241393 + 0.134455i) q^{67} +(-0.247582 + 0.271585i) q^{68} +(-1.30318 + 2.61715i) q^{72} +(-0.288130 + 1.01267i) q^{73} +(0.629488 + 1.87814i) q^{75} +(-1.42871 - 0.711414i) q^{76} +(2.78663 - 3.69010i) q^{81} +(0.457413 + 0.0211475i) q^{82} +(0.134455 - 0.963876i) q^{83} +(0.456541 - 1.03397i) q^{86} +(-1.67148 + 1.03494i) q^{88} +(-0.0373089 - 0.806980i) q^{89} +(-1.40065 + 1.40065i) q^{96} +(-1.18375 + 0.982973i) q^{97} +(-0.961826 - 0.273663i) q^{98} +(5.35961 - 2.07632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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